The generator matrix

1 0 0 0 0 0 0 1 1 1 2 0 0 2 1 1 2 2 1 1 1 1 1 2 1 1 1 0 1 0 0 1 1 0 1 1 2 2 1 1 2 2 1 0 2 1 1 0 2 0 2 2 1 2 1 2 2 1 2 2 1 0 1 1 1 1 2 2 1 2 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1
0 1 0 0 0 0 0 0 0 0 0 1 2 1 1 1 1 1 1 1 3 3 2 1 0 0 1 2 3 2 1 1 0 0 3 1 1 0 3 3 2 1 2 1 0 1 2 1 1 1 2 1 1 0 0 1 1 3 1 1 0 2 1 0 3 3 1 1 3 2 0 3 2 3 1 2 1 2 0 2 1 1 3 0 1 0 0
0 0 1 0 0 0 0 0 0 0 0 0 1 3 1 3 1 3 1 1 2 0 3 2 3 3 0 1 2 1 1 1 1 1 0 0 2 2 2 1 1 2 2 0 1 3 3 3 3 1 1 1 2 2 0 1 2 2 2 1 0 2 3 0 1 1 2 2 3 0 3 1 2 2 3 2 0 0 1 0 0 3 1 3 1 1 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 2 2 2 2 0 2 0 2 0 2 2 1 3 3 1 1 1 3 1 3 3 1 1 1 1 2 3 2 1 2 1 0 0 3 1 0 3 2 0 1 1 2 0 1 3 0 1 1 2 0 1 3 0 0 3 1 1 3 0 3 2 0 3 0 2 2 3 0
0 0 0 0 1 0 0 0 1 1 1 2 0 1 0 3 0 1 3 2 1 1 0 3 1 2 2 2 0 3 0 1 0 1 0 1 3 0 2 0 2 3 3 2 3 3 2 1 1 0 2 1 0 1 3 3 0 2 1 0 1 0 2 1 1 0 2 3 2 2 3 3 0 1 3 1 0 1 0 1 1 1 3 0 0 1 0
0 0 0 0 0 1 0 1 0 1 3 2 0 3 0 1 1 0 2 3 2 1 0 3 0 1 0 1 1 3 1 1 3 0 3 3 0 3 2 3 2 3 0 0 2 0 2 1 3 2 3 0 2 0 3 2 0 3 0 1 2 1 1 3 1 0 1 2 2 0 1 0 1 1 3 2 1 3 1 2 2 2 0 2 3 0 0
0 0 0 0 0 0 1 1 3 2 1 1 1 2 3 3 1 3 2 0 2 1 2 0 1 1 3 2 0 1 2 0 2 3 3 0 2 1 0 3 0 3 1 2 1 2 1 2 1 2 3 2 3 2 1 1 1 1 3 1 0 1 0 2 2 3 1 2 2 1 0 0 0 1 3 2 1 3 3 2 0 1 3 3 3 0 1
0 0 0 0 0 0 0 2 2 0 2 2 2 0 2 2 2 2 0 0 0 2 0 0 2 2 2 0 0 2 0 0 0 2 2 0 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 2 0 2 2 2 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 0 0 2 2 0

generates a code of length 87 over Z4 who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+38x^71+131x^72+230x^73+353x^74+492x^75+601x^76+820x^77+906x^78+1040x^79+1249x^80+1370x^81+1426x^82+1560x^83+1603x^84+1670x^85+1854x^86+1794x^87+1889x^88+1842x^89+1839x^90+1662x^91+1436x^92+1298x^93+1108x^94+1094x^95+952x^96+740x^97+552x^98+414x^99+275x^100+200x^101+138x^102+90x^103+49x^104+18x^105+14x^106+8x^107+5x^108+4x^109+2x^110+1x^152

The gray image is a code over GF(2) with n=174, k=15 and d=71.
This code was found by Heurico 1.10 in 157 seconds.